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The uncertainties in the parameter error covariance matrix 
and
the need to adjust the flux based on measurements for a particular
area will undoubtedly require users to produce their own fine
tuning of the heat and fresh water fluxes. To this end, we provide
users of UWM/COADS with sensitivity fields associated
with each of the tuning parameters discussed in this section.
For example, the net heat flux can be written as
The corresponding sensitivity fields are
The sensitivity fields 
, 
and 
are equal to
, 
and 
which are the full unconstrained fields
already included in UWM/COADS. The other sensitivity fields are
computed either from individual observations with climatology and
anomalies analyzed the same way as the other UWM/COADS fields (
and 
), or derived from analyzed fields (
).
In order to produce constrained estimates of the individual heat flux
components, one can calculate
where 
denotes the unconstrained estimate of the heat flux
component as included in UWM/COADS. Likewise, constrained evaporation
and precipitation fields can be computed from
The parameters in Tables 11-13 can be
used to produce several versions of the constrained heat and fresh
water fluxes. In addition, new values for the tuning parameters can be
obtained as follows. The sensitivity matrix 
can be computed by
integrating the sensitivity fields 
at a given latitude, e.g.,
(assuming 
is the 
th parameter). The new tuning parameters
can be obtained by solving (55), given estimates for
the parameter error covariance matrix 
and oceanographic
measurements 
with error covariance matrix 
.